The present invention relates to a new and distinct cultivar of chrysanthemum plant, botanically known as Chrysanthenum×morifolium Ramat., commercially grown as a garden mum, and herein after referred to by the cultivar denomination ‘Zanmusunbur’. ‘Zanmusunbur’ is a product of a breeding and selection program for outdoor pot mums (garden mums) which had the objective of creating new chrysanthemum cultivars with a semi-double type flower, a natural season flower date around September 10 (week 37); blooming for a period of 5 weeks. ‘Zanmusunbur’ is a seedling resulting from a crossing program, set up by a previous breeder, and which records are unknown to the inventor. The new and distinct cultivar was discovered and selected as a flowering plant by Wilhelmus Bernardus Blom on a cultivated field in Rijsenhout, The Netherlands in 2003. The first act of asexual production of ‘Zanmusunbur’ was accomplished when vegetative cuttings from the initial selection in 2003 were propagated further in a controlled environment in Rijsenhout, The Netherlands. The new cultivar has been found to retain its distinctive characteristics through successive propagations.